In-plane elastic wave propagation in nanoscale periodic layered piezoelectric structures

Wave propagation in nanoscale piezoelectric structures is much more complex than in macro-sized elastic structures. This study is devoted to the analysis of in-plane elastic waves propagating normally and obliquely in nanoscale periodic layered piezoelectric structures. The equations of wave motion which take both the piezoelectric effect and the nanoscale size-effect into account are solved numerically. The transfer matrix method based on the nonlocal piezoelectric continuum theory is used to calculate the localization factor which characterizes the band structures. Additionally, the wave transmission spectra are also computed by the stiffness matrix method. The piezoelectric effect (i.e., the piezoelectric constants) and the size-effect (i.e., R, the influences of the ratio of the internal to external characteristic lengths) on the cut-off frequency and the wave propagation characteristics are discussed in details. The influence of the mode conversion on band-gaps and the influence of R on the mode conversion are analyzed.